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Guided Notes and Study Guide SCIENTIFIC NOTATION 1.) Defining scientific notation: A number written in scientific notation is a number greater than or equal to but less than multiplied by a power of . Scientific notation is written as , where 1 < a < 10. Ex. 1: Ex. 2: Ex. 3: Ex 4: 2.45 x 108 0.0543 x 104 3 x 10-5 21.3 x 10-6 in scientific notation. in scientific notation. in scientific notation. in scientific notation. 2.) Scientific to Standard Notation: STEP 1: Determine whether the power of 10 is or . If the power of 10 is , move the decimal that many units to the . If the power of 10 is , move the decimal that many units to the . STEP 2: Add in any and that are needed to indicate place value. Ex. 1: Ex. 2: 2.45 x 108 = 3 x 10-5 = The power of 10 is . It is so I will move the decimal point places to the . I will add zeros and commas. The power of 10 is . It is so I will move the decimal point to the . I will add zeros. places 3.) Standard to Scientific Notation: STEP 1: Move the decimal so the number is greater than or equal to but less than . STEP 2: Count the number of decimal places moved in STEP 1. If the decimal point was moved to the or the original number was , the count is . If the decimal point was moved to the or the original number was , the count is . STEP 3: Write as a product of the (found in STEP 1) and raised n to the power of the count from STEP 2(in the form a x 10 ). Ex. 1: Ex. 2: 30,500,000 3.0500000 x 10n= I moved the decimal point the , so the count is a= and n = 0.000781 00007.81 x 10n = I moved the decimal point the , so the count is a= and n = places to . . places to . . 4.) Multiplication with Scientific Notation: To multiply numbers in scientific notation, (1) the numbers; (2) the exponents; (3) multiply the product from STEP 1 by 10n, where n is the sum from STEP 2; and (4) rewrite the answer in correct scientific notation form (the first number must be greater than or equal to but less than ). Ex: Evaluate: (5 x 10-8)(2.9 x 102) = (5 x 2.9)(10-8 x 102) = 14.5 x 10-8 + 2 = 14.5 x 10-6 = (1.45 x 101) x 10-6 = 1.45 x (101 x 10-6) = 1.45 x (101+(-6)) = 1.45 x 10-5 or 0.0000145 Combine like terms. Multiply numbers& add exponents. 14.5 = 1.45 x 101. Combine like terms. Add exponents. Scientific &standard notation. 5.) Division with Scientific Notation: To divide numbers in scientific notation, (1) the numbers; (2) the exponents; (3) multiply the quotient from STEP 1 by 10n, where n is the difference from STEP 2; (4) rewrite the answer in correct scientific notion form (the first number must be greater than or equal to but less than ). Ex: Evaluate: = 1.2789 109 5.22 105 = 0.245 x 104 1.2789 x 109 5.22 x 105 = (2.45 x 10-1) x 104 = 2.45 x (10-1 x 104) = 2.45 x 10(-1)+4 = 2.45 x 103 or 2450 Combine like terms. Multiply numbers & subtract exponents. 0.245 = 2.45 x 10-1 Combine like terms. Add exponents. Scientific & standard notation. Guided Notes and Study Guide SCIENTIFIC NOTATION 1.) Defining scientific notation: A number written in scientific notation is a decimal number greater than or equal to 1 but less than 10 multiplied by a power of 10 . Scientific notation is written as a x 10n , where 1 < a < 10. Ex. 1: Ex. 2: Ex. 3: Ex 4: 2.45 x 108 0.0543 x 104 3 x 10-5 21.3 x 10-6 is in scientific notation. is not in scientific notation. is in scientific notation. is not in scientific notation. 2.) Scientific to Standard Notation: STEP 1: Determine whether the power of 10 is positive or negative . If the power of 10 is positive , move the decimal that many units to the right . If the power of 10 is negative , move the decimal that many units to the left. STEP 2: Add in any zeros and commas that are needed to indicate place value. Ex. 1: 2.45 x 108 = 245,000,000 The power of 10 is 8 . It is positive so Iwill move the decimal point 8 places to the right. I will add zeros and commas. Ex. 2: 3 x 10-5 = 0.00003 The power of 10 is -5 . It is negative so I will move the decimal point 5 places to the left . I will add zeros. 3.) Standard to Scientific Notation: STEP 1: Move the decimal so the number is greater than or equal to 1 but less than 10. STEP 2: Count the number of decimal places moved in STEP 1. If the decimal point was moved to the left or the original number was greater than one, the count is positive . If the decimal point was moved to the right or the original number was less than one, the count is negative . STEP 3: Write as a product of the number (found in STEP 1) and 10 raised n to the power of the count from STEP 2(in the form a x 10 ). Ex. 1: 30,500,000 3.0500000 x 10n= 3.05 x 107 I moved the decimal point 7 places to the left , so the count is positive. a = 3.05 and n = 7 . Ex. 2: 0.000781 00007.81 x 10n = 7.81 x 10-4 I moved the decimal point 4 places to the right ,so the count is negative . a = 7.81 and n = -4 . 4.) Multiplication with Scientific Notation: To multiply numbers in scientific notation, (1) multiply the numbers; (2) add the exponents; (3) multiply the product from STEP 1 by 10n, where n is the sum from STEP 2; and (4) rewrite the answer in correct scientific notation form (the first number must be greater than or equal to 1 but less than 10 ). Ex: Evaluate: (5 x 10-8)(2.9 x 102) = (5 x 2.9)(10-8 x 102) = 14.5 x 10-8 + 2 = 14.5 x 10-6 = (1.45 x 101) x 10-6 = 1.45 x (101 x 10-6) = 1.45 x (101+(-6)) = 1.45 x 10-5 or 0.0000145 Combine like terms. Multiply numbers& add exponents. 14.5 = 1.45 x 101. Combine like terms. Add exponents. Scientific &standard notation. 5.) Division with Scientific Notation: To divide numbers in scientific notation, (1) divide the numbers; (2) subtract the exponents; (3) multiply the quotient from STEP 1 by 10n, where n is the difference from STEP 2; (4) rewrite the answer in correct scientific notion form (the first number must be greater than or equal to 1 but less than 10 ). Ex: Evaluate: = 1.2789 109 5.22 105 = 0.245 x 104 1.2789 x 109 5.22 x 105 = (2.45 x 10-1) x 104 = 2.45 x (10-1 x 104) = 2.45 x 10(-1)+4 = 2.45 x 103 or 2450 Combine like terms. Multiply numbers & subtract exponents. 0.245 = 2.45 x 10-1 Combine like terms. Add exponents. Scientific & standard notation.